Integrability for the spectrum of Jordanian AdS/CFT
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| Format: | Preprint |
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2025
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| _version_ | 1866912962704310272 |
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| author | Driezen, Sibylle Levkovich-Maslyuk, Fedor Molines, Adrien |
| author_facet | Driezen, Sibylle Levkovich-Maslyuk, Fedor Molines, Adrien |
| contents | Jordanian deformations offer rare integrable realisations of non-AdS holography, whose solvability methods differ from conventional AdS/CFT examples. Here we study the $\mathfrak{sl}(2,R)$ sector of the Jordanian deformed $AdS_5\times S^5$ string and its weak-coupling spin chain counterpart: the $\mathrm{XXX}_{-1/2}$ model with a non-abelian Jordanian Drinfel'd twist. While the twist breaks the usual highest-weight structure that underlies conventional Bethe ansätze, we show that the complete spectrum remains solvable within the Baxter framework. We argue that the functional form of the $TQ$-relation is unchanged, yet the structure of the $Q$-functions is nontrivially modified. This allows us to obtain analytic expressions at arbitrary spin chain length $J$, which match the deformed string spectrum at the one-loop level and to subleading order in the large-$J$ expansion, despite the severely reduced symmetry. Our results provide nontrivial tests of the Jordanian AdS/CFT correspondence and lay the groundwork for implementing the Separation of Variables program in non-abelian Drinfel'd-twisted models. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_11521 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Integrability for the spectrum of Jordanian AdS/CFT Driezen, Sibylle Levkovich-Maslyuk, Fedor Molines, Adrien High Energy Physics - Theory Statistical Mechanics Mathematical Physics Exactly Solvable and Integrable Systems Jordanian deformations offer rare integrable realisations of non-AdS holography, whose solvability methods differ from conventional AdS/CFT examples. Here we study the $\mathfrak{sl}(2,R)$ sector of the Jordanian deformed $AdS_5\times S^5$ string and its weak-coupling spin chain counterpart: the $\mathrm{XXX}_{-1/2}$ model with a non-abelian Jordanian Drinfel'd twist. While the twist breaks the usual highest-weight structure that underlies conventional Bethe ansätze, we show that the complete spectrum remains solvable within the Baxter framework. We argue that the functional form of the $TQ$-relation is unchanged, yet the structure of the $Q$-functions is nontrivially modified. This allows us to obtain analytic expressions at arbitrary spin chain length $J$, which match the deformed string spectrum at the one-loop level and to subleading order in the large-$J$ expansion, despite the severely reduced symmetry. Our results provide nontrivial tests of the Jordanian AdS/CFT correspondence and lay the groundwork for implementing the Separation of Variables program in non-abelian Drinfel'd-twisted models. |
| title | Integrability for the spectrum of Jordanian AdS/CFT |
| topic | High Energy Physics - Theory Statistical Mechanics Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2511.11521 |